Solved Integral Exercises

A collection of fully worked and explained exercises on integral calculus.

Exercise	$$ \int x \cdot \cos x \ dx $$
Exercise	$$ \int (x+2)^3 \ dx $$
Exercise	$$ \int \frac{9x-3}{x^2+1} \ dx $$
Exercise	$$ \int \frac{1 + e^{ \sqrt{x}}}{\sqrt{x}} \ dx $$
Exercise	$$ \int 2x \cdot e^{x^2} \ dx $$
Exercise	$$ \int 2x(1+x^2)^5 \ dx $$
Exercise	$$ \int x^{-\frac{1}{3}} \ dx $$
Exercise	$$ \int x^{- \frac{2}{3}} \ dx $$
Exercise	$$ \int \frac{1-x^2}{x^2+1} \ dx $$
Exercise	$$ \int \frac{1}{2+x^2} \ dx $$
Exercise	$$ \int \frac{1}{(1+x)x} \ dx $$
Exercise	$$ \int e^{5x} dx $$
Exercise	$$ \int \frac{e^{x+1}}{3+e^x} \ dx $$
Exercise	$$ \int \frac{x+2}{x^3-x^2-2x} \ dx $$
Exercise	$$ \int \frac{x-2}{x^3-7x-6} \ dx $$
Exercise	$$ \int \frac{1}{x \sqrt{2x-1}} dx $$
Exercise	$$ \int \frac{1}{\sqrt{x}} - \frac{1}{\sqrt{1-x^2}} dx $$
Exercise	$$ \int \frac{1}{x \sqrt{1-\log^2 x}} \ dx $$
Exercise	$$ \int \frac{e^{\sqrt{2x+1}}}{\sqrt{2x+1}} \ dx $$
Exercise	$$ \int \frac{e^{2x}}{3-e^x} dx $$
Exercise	$$ \int \frac{1}{1+e^{3x}} \ dx $$
Exercise	$$ \int \frac{\cos \sqrt{x}}{\sqrt{x}} \ dx $$
Exercise	$$ \int \sin^3 (x) \cdot \cos(x) \ dx $$
Exercise	$$ \int \frac{\sin x + \cos x}{\sin x - \cos x} \ dx $$
Exercise	$$ \int \frac{e^{\sqrt{x}} \cdot \cos(e^{\sqrt{x}} ) }{\sqrt{x}} \ dx $$
Exercise	$$ \int 2 \cdot \tan^2(x) - 1 \ dx $$
Exercise	$$ \int \frac{1}{\tan^2(x)} \ dx $$
Exercise	$$ \int \frac{1}{\tan^3(x)} \ dx $$
Exercise	$$ \int \frac{x-1}{x^2+3x} \ dx $$
Exercise	$$ \int \frac{2x+5}{(x+1) \cdot (x+3)^2 } \ dx $$
Exercise	$$ \int \frac{x^3+2x-3}{x^2+2x+1} \ dx $$
Exercise	$$ \int \frac{x^2-3}{x^3-4x^2+5x-2} \ dx $$
Exercise	$$ \int \frac{x^2}{4x^2+1} \ dx $$
Exercise	$$ \int \frac{1}{x^2+x^4} \ dx $$
Exercise	$$ \int \frac{( \sin x - \cos x)^2}{\cos^2 x} \ dx $$
Exercise	$$ \int \frac{\cos x}{2- \cos^2 x} \ dx $$
Exercise	$$ \int \frac{3e^{3x}}{6-e^{3x}} \ dx $$
Exercise	$$ \int \frac{ \log^2[\sin(x)] }{\sin^2(x)} \cdot \sin(x) \ dx $$
Exercise	$$ \int \frac{1}{(1+x^2) \cdot \arctan x} \ dx $$
Exercise	$$ \int \cot (ax+b) \ dx $$
Exercise	$$ \int_0^{\frac{1}{2}} \sqrt{1-x^2} \ dx $$
Exercise	$$ \int_1^{\sqrt{e}} \frac{\log(x)-2}{x[\log^2(x)-1] } \ dx $$